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A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes
Department of Mathematics, The Florida State University, Tallahassee, USA.
Mathematisches Institut, Universität zu Köln, Köln, Germany.ORCID iD: 0000-0002-5902-1522
Mathematisches Institut, Universität zu Köln, Köln, Germany.
Mathematisches Institut, Universität zu Köln, Köln, Germany.
2016 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 139, p. 148-160Article in journal (Refereed) Published
Abstract [en]

We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free- stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 139, p. 148-160
Keywords [en]
discontinuous Galerkin spectral element method, summation-by-parts, moving mesh, arbitrary Lagrangian-Eulerian, energy stable, free-stream preservation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-156862DOI: 10.1016/j.compfluid.2016.05.023ISI: 000387298600013Scopus ID: 2-s2.0-84992187569OAI: oai:DiVA.org:liu-156862DiVA, id: diva2:1315749
Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-21Bibliographically approved

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